About this representation

Group J3
Group generators Standard generators
Number of points 23256
Primitivity information Primitive
Transitivity degree 1
Rank 28
Suborbit lengths 1, 80, 135, 180, 5405, 7207, 108010, 21602
Contributed by Not recorded

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This representation is available in the following formats:

MeatAxe a b
MeatAxe binary a b
GAP a b
GAP a, b
Magma a, b

On conjugacy classes

Conjugacy class Fixed points Cycle type
1A 23256
2A 136 211560
3A 81 37725
3B 9 37749
4A 4 266, 45780
5A 1 54651
5B 1 54651
6A 1 240, 345, 63840
8A 2 2, 433, 82890
9A 0 33, 92583
9B 0 33, 92583
9C 0 33, 92583
10A 1 527, 102312
10B 1 527, 102312
12A 1 3, 420, 622, 121920
15A 1 516, 151545
15B 1 516, 151545
17A 0 171368
17B 0 171368
19A 0 191224
19B 0 191224

Checks applied

Check Description Date Checked by Result
Presentation Check against the relations in a presentation. If this test passes, then the group is of the correct isomorphism type, and the generators are those stated. Note that the presentation itself is not checked here. Aug 2, 2006 certify.pl version 0.05 Pass
Semi-presentation Check against a semi-presentation. If this fails, then the representation is not on standard generators, and may generate the wrong group. Note that the semi-presentation itself is not checked here. Jul 4, 2006 certify.pl version 0.05 Pass
Order Check that the elements generate a group of the correct order. Jul 18, 2006 permanalyse version 0.03 Pass
Number of points Check whether the permutation representation is acting on the stated number of points. Jul 4, 2006 certify.pl version 0.05 Pass
Files exist Check whether files exist (where stated). Jul 4, 2006 certify.pl version 0.05 Pass